In this, the first of the five major categories of this course, the topics covered include:
Limits of functions (including one-sided limits)
• An intuitive understanding of the limiting process.
• Calculating limits using algebra.
• Estimating limits from graphs or tables of data.
Asymptotic and unbounded behavior
• Understanding asymptotes in terms of graphical behavior.
• Describing asymptotic behavior in terms of limits involving infinity.
• Comparing relative magnitudes of functions and their rates of change (for example,
contrasting exponential growth, polynomial growth, and logarithmic growth).
Continuity as a property of functions
• An intuitive understanding of continuity. (The function values can be made as
close as desired by taking sufficiently close values of the domain.)
• Understanding continuity in terms of limits.
• Geometric understanding of graphs of continuous functions (Intermediate
Value Theorem and Extreme Value Theorem).